Ten-Yen:  the enclosure challenge

Here is a different sort of challenge. Any one color—the U, T and Z groups—can be enclosed with the other two colors. The enclosure must be complete, the sides fully closed, not just by corners. This is an example of incomplete enclosure:

Below are examples of full enclosures for each of the three color groups. The T and U group show a perimeter of 28 units; the Z group has a 26. Can you do better? What's your shortest perimeter? Since it is not possible to enclose a group and have all pieces fit within their 6x6 tray, we know that 26 is the minimum. If you find a minimum enclosure for any of the 3 groups different from these, send us your solution and we'll add your results here.


In October 2014, Robert Vermillion was the first to find minimum enclosures for the U and T groups and won a prize:


And he did us one better by enclosing the Z group with all colors joined:

George Sicherman explored the other extreme—enclosures with the longest perimeter, and with colors grouped to boot. Here are his first two results—a 32-surround for the Z group, and an incredible 34-surround for the T group. We're still waiting to find one for the U group.


Send your solutions to: Enclosure.

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